1.In a medium pot, heat the vegetable oil over medium heat. Add the onion, garlic, chile, ginger, lemongrass, kaffir, and paste and cook, stirring frequently, for 5 minutes, or until onions are softened.
2.Add chicken broth and bring to a boil. Reduce heat and simmer uncovered for 30 minutes.
3.Strain out the aromatics and discard. Add in coconut milk, chicken, and mushrooms. Simmer until chicken pieces are just cooked through.
4.Add fish sauce, sugar, and lime juice, plus more of each to taste. Cook 2 minutes.
5.Add green onions and cilantro. Ladle into serving bowls and serve.